GPS receivers and navigation systems used in aircraft utilize GPS satellite signals and information to calculate a navigation solution. A navigation solution represents the calculated position of the aircraft in three dimensional space. A navigation solution can also include heading and speed information.
Navigation solution integrity is the guarantee, to some specified high confidence level, that some scalar measure of navigation solution position error (e.g., horizontal, vertical, crosstrack, etc.) is below a threshold called the "protection level". The function or device which ensures navigation solution integrity both computes this protection level and continuously monitors a variable which is indicative of navigation solution integrity. The specified certainty to which the integrity monitor ensures navigation solution integrity is called the Probability of Detection. Also associated with the integrity monitor is a False Alarm Rate.
Receiver Autonomous Integrity Monitoring (RAIM) is one method of monitoring the integrity of a GPS navigation solution for position and time. The objective of RAIM is to protect the navigation solution against the effect of an unbounded pathological bias in any one measurement (i.e., from a GPS satellite signal) used as an input to the navigation solution. RAIM accomplishes this by monitoring the consistency of redundant position measurement data in an over-determined navigation position solution.
RAIM offers two levels of integrity capability. These differ in terms of action each undertakes following detection of a pathological measurement error bias. The first of these integrity capabilities, called RAIM Fault Detection (FD), merely alerts the user that GPS navigation is no longer operating with integrity. The second of these integrity levels, called RAIM Fault Detection and Exclusion (FDE), attempts to continue GPS navigation with integrity following a detection. FDE attempts to identify the faulted measurement and to exclude it from use in the navigation solution. If the faulted measurement cannot be identified with a certainty equal to the specified Probability of Detection, then the user is alerted that GPS navigation is no longer operating with integrity.
The performance requirements for RAIM FD in civilian aviation are specified in RTCA DO-208 and in FAA TSO C129 and C129a. The performance requirements for RAIM FDE in civilian aviation are specified in RTCA DO-229. These documents are herein incorporated by reference. The basics of RAIM have been extensively described in the literature. Conceptually, generic RAIM embraces the following principles:
(1) Each of the redundant measurements contains an error bias which, after application of all deterministic corrections, is independent of the bias in any other measurement and which can be pessimistically modeled as a zero-mean Gaussian random variable with known variance.
(2) One measurement may also contain an unbounded pathological bias. The probability of occurrence of this pathological bias in any measurement is independent of that in any other measurement and is sufficiently small such that the probability of simultaneous existence of pathological biases in two or more measurements is negligible.
(3) It is possible to posit m+1 hypotheses H.sub.j, j=0 to m, where H.sub.0 is the so-called null hypothesis that no pathological bias exists, Hj is the hypothesis that a non-zero pathological bias exists on measurement j, and m is the number of measurements. Exactly one of these hypotheses is true at any time.
(4) The FDE test statistic, or variable monitored by RAIM as an indicator of navigation solution integrity, is related to the bias which remains in the measurement residual vector when it is referenced to the Least Squares navigation solution. The Least Squares navigation solution is that which minimizes this bias. The measurement residual vector referenced to the Least Squares navigation solution is referred to as the Least Squares measurement residual vector.
(5) From the Least Squares measurement residual vector it is possible to compute the relative probability of each of the hypotheses H.sub.j, j=0 to m, conditioned upon the value of the measurement residual vector.
(6) Based upon the characteristics of the nominal measurement error vector and a pathological bias on measurement j, it is possible to derive a probability distribution for the navigation solution error state vector conditioned upon each of the hypotheses Hj, j=0 to m.
(7) It is possible to define m-4 states, additional to the four navigation solution error states of receiver position and receiver clock bias, such that the value of all m states is uniquely related to the set of bias errors in the m measurements. These m-4 additional states, called parity states, define an (m-4) dimensional vector space called parity space. The concepts of parity space and parity states are understood in the literature.
It is possible to select a boundary in parity space such that the magnitude of the parity vector exceeds this bound with a very small probability known as the Probability of False Alarm (PFA). This limit is called the RAIM detection threshold. Note that if the parity vector magnitude exactly equals the detection threshold, then the probability of the null hypothesis approximates PFA.
(8) From the navigation solution error probability distribution described in item (6), from the formulae for the probability of hypotheses Hj described in item (5), and from analysis the sensitivity of the integrity metric and the navigation solution to a pathological bias in a particular measurement j, it is possible to establish an upper bound upon the navigation error at the point of RAIM detection with some high level of confidence. This limit is the RAIM protection level for fault detection conditioned upon hypothesis Hj, j=0 to m. The high confidence level with which it bounds navigation error is the RAIM Probability of Detection.
(9) If, after detection, the probability of any one hypothesis Hj, j=1 to m, is greater than 0.999, then the Receiver will stop using measurement j for navigation, and GPS navigation may continue uninterrupted. Otherwise, the RAIM function issues an alert indicating that high integrity GPS navigation is not available.
A variety of RAIM techniques which implement the above principles have been proposed and analyzed in the literature. These techniques are essentially equivalent. A RAIM FDE methodology which provides improved integrity monitoring relative to these prior art RAIM techniques would be a significant improvement in the field.